1. Field of the Invention
This application relates to the field of image processing and/or data processing.
2. Description of the Related Technology
For many display devices, there is a nonlinear relationship between the brightness of a pixel as it appears on the screen, and the numerical value of that pixel. This nonlinear relationship is approximately a power function, wherein the displayed brightness is the pixel value raised to a power of a numeral referred to herein as gamma, which is typically a non-integer between 1 and 3. In various image processing applications, a process sometimes called gamma translation is performed, raising a pixel value to a defined power. In some situations, a previously performed gamma translation is reversed, which also involves raising a pixel value to a defined power. For convenience, the defined power is always referred to herein as gamma, regardless of its relationship between the image data values and the visual characteristics of the display device.
Conventionally, a lookup table (“LUT”) is used in these processes. The image data value, represented by an appropriately sized binary number, is used as an index pointing to a table entry where the translated representation resides. A LUT is associated with a particular defined power. If several defined powers are needed, then several LUTs 12a-12n, each associated with one defined power, are required as illustrated in FIG. 1. This approach requires allocating substantial system resources for LUTs, especially when the number of gammas is large. For example, each LUT may need to be stored in expensive one-time programmable memory. Further, such an approach can only work with a limited number of defined powers for which a corresponding LUT is established. To support a new defined power, the system has to be revised to incorporate a new LUT.
Iterative algorithms based on Newton's method may also be used to compute a number to any defined power using only arithmetic operations. However, these methods require a relatively large number of calculations, and require time and processing power that is also expensive to provide for small displays such as mobile phones and the like.
Another way to raise a number to any defined power is to use piecewise linear approximations, which combine smaller LUTs with arithmetic operations. However, this approach achieves greater accuracy at the expense of increasing the number of arithmetic operations.
Therefore, it is desirable to develop a method and system of raising an image data value to a power that uses a fixed, and preferably small number of LUTs and that works with any defined data and power value. Such a method and system may be equally applied to a variety of applications to raise a number to a power of any real number.